§ 91.508 - Cumulative Sum (CumSum) procedure.

§ 91.508 Cumulative Sum (CumSum) procedure.

(a) Manufacturers must construct the following CumSum Equation for HC + NO_X for each engine family. Test results used to calculate the variables in the CumSum Equation must be final deteriorated test results as defined in § 91.509(c).

C_i = max[0 0R (C_i-1 + X_i − (FEL + F))]

Where:

C_i = The current CumSum statistic

C_i-1 = The previous CumSum statistic. Prior to any testing, the CumSum statistic = 0 (i.e. C₀ = 0)

X_i = The current emission test result for an individual engine

FEL = Family Emission Limit

F = 0.25 × σ

After each test, C_i is compared to the action limit, H, the quantity which the CumSum statistic must exceed, in two consecutive tests, before the engine family may be determined to be in noncompliance for purposes of § 91.510.

H = The Action Limit. It is 5.0 × σ, and is a function of the standard deviation, σ.

σ = is the sample standard deviation and is recalculated after each test.

(b) After each engine is tested, the CumSum statistic shall be promptly updated according to the CumSum Equation in paragraph (a) of this section.

(c)

(1) If, at any time during the model year, a manufacturer amends the application for certification for an engine family as specified in paragraph (a) of § 91.122 by performing an engine family modification (i.e. a change such as a running change involving a physical modification to an engine, a change in specification or setting, the addition of a new configuration, or the use of a different deterioration factor) with no changes to the FEL, all previous sample size and CumSum statistic calculations for the model year will remain unchanged.

(2) If, at any time during the model year, a manufacturer amends the application for certification for an engine family as specified in paragraph (a) of § 91.122 by modifying its FEL as a result of an engine family modification, the manufacturer must continue its calculations by inserting the new FEL into the sample size equation as specified in § 91.506(b)(1) and into the CumSum equation in paragraph (a) of this section. All previous calculations remain unchanged. If the sample size calculation indicates that additional tests are required, then those tests must be performed. The CumSum statistic recalculation must not indicate that the family has exceeded the action limit for two consecutive tests. The manufacturer's final credit report as required by § 91.210 must break out the credits that result from each FEL and corresponding CumSum analysis for each FEL set.

(3) If, at any time during the model year, a manufacturer amends the application for certification for an engine family as specified in paragraph (a) of § 91.122 by modifying its FEL without performing an engine modification, all previous sample size and CumSum statistic calculations for the model year must be recalculated using the new FEL. If the sample size calculation indicates that additional tests are required, then those tests must be performed. The CumSum statistic recalculation must not indicate that the family has exceeded the action limit for two consecutive tests.

(4) If, at any time after the end of the model year but prior to the manufacturer's final credit report submittal as specified in § 91.210, a manufacturer changes an FEL for an entire family, or for an affected part of the year's production, as specified in paragraph (a) of § 91.122, in cases where there were one or more mid-year engine family modifications, all previous sample size and CumSum statistic calculations for the model year, or part of the model year affected by an engine family change, must be recalculated using the new FEL. The sample size equation must not indicate a larger number of tests than were appropriately performed using the previous FEL and the CumSum statistic recalculation must not exceed the action limit in two consecutive tests. The manufacturer's final credit report as required by § 91.210 must break out the credits that result from each FEL and corresponding CumSum analysis for each FEL set.